Advanced Dungeons & Dragons was developed from the Dungeons & Dragons game in the late 1970s. It allowed for more versatility in making characters and more detail and depth than the basic game had. Not to be confused with Adult Dungeons and Dragons. That would be a FATAL mistake.

D&D went all over the place. There were tons of books and finding rules for everything was sometimes a chore. Especially the options that separated race and class, alignments, and finding all the monsters stats could send you through 30 books.Gary Gygax saw fit to begin compiling all of the info into easy to search, themed books.

He started with the Monster Manual (1977), going through all of the books he could find and compiling them into one book that was usable in D&D, alphabetized, with illustrations and in hardback. The book was still usable with D&D so nobody raged at this.

Next came the Players Handbook (PHB) in 1978, which compiled all the races found in Blackmoor and Greyhawk, and all of the classes. It eased up on the default classes for non-humans. It added more options, detail and equipment, and allowed you to create a character that was technically usable in D&D. It was still compatible and there was no rage.

The scale went from 10 to -10 on armor class, this being a choice made to incorporate the d20 in an approximation of Chainmail's combat system. Armor class was essentially representative of a bonus to the attacker. Unarmored targets gave a 10 point bonus, Heavily armored targets gave less of a bonus, and super heavily armored (or extremely agile) targets could impose negatives to the attack roll.

The meat and potatoes of the game along with all those nifty new rules in the PHB, came in the DMG. Guidelines for creating dungeons, populating them, filling them with treasure, combat matrices for characters and monsters, and wrapped all the stuff that seemed arbitrary in the MM and DMG up into a solid RPG.

Advanced Dungeons & Dragons played much like the original D&D game (not to be confused with Basic, which was not compatible) which consisted of playing the role of your character, and resolving actions with a chance of failure by using dice.
Players first create a character using the rules found in the PHB. The Dungeon Master then inserts the characters as appropriate in his campaign, whether homemade or manufactured world or a simple module or one shot adventure.

Depending on how you count, AD&D 1E came out in 1977 or 1979. It lasted to 1989, which means it lived to the ripe old age of 10-12, which is actually pretty old for an RPG (albeit, not one that costs so much, to be fair. Other RPGs that offer core in a single volume are usually much cheaper than AD&D, even then). It saw many issues in that time, from being falsely linked to a boy's disappearance in 1979, being linked to a suicide (google Patricia Pulling) and being the centerpiece for the now infamous Chick Tract: Dark Dungeons. Still through it all, TSR saw money come in. When issues arose in the company between Gygax and two other board members, one of the board members sold his stock to an ingrateful manager that Gygax had hired, and rather than ride a ship he thought would sink, Gygax sold his stock to the rapacious she-bitch as well. In 1989, the decision came to publish a new version of AD&D, ostensibly to limit Gygax's royalties.

This edition added a whole lot of modular rules and fluff material. The core methodology of 1E was still in place, slightly more basic in scope. It also added a huge amount of optional rules from Unearthed Arcana and the Survival Guide books. For the most part, the core books work as described above, so this is what's different:

2E took the combat matrices and made them uniform in function. Every class or kit in the game falls under one of 4 categories, and each category has a different rate of improvement. Fighters, obviously, get the best rate, while non-physical fighters get the worst. The statistic used to implement these categories was called THAC0.

THAC0 stands for To Hit Armor Class 0 (zero); it's the minimum number you needed to roll on a d20 in order to hit something with AC 0 (which means the lower your THAC0, the better for you). To handle other armor classes, you subtracted the target's AC from your character's THAC0, and then tried to roll at least this number. DMs often did not share the enemy's AC, in which case you would roll a d20, and subtract it from your THAC0 to show the lowest AC that you could hit. wait for the DM to tell you if you hit since it's his job.

Opinions of this mechanic are divided; some say it's overly complicated and non-intuitive (negative ACs being a common argument), while others don't mind all the basic subtraction (also, thac0 progression can just be thought of as to-hit bonus, negating any math besides being able to reverse your added result in order to know what AC you hit). Others just say that no matter how retarded it is, it's preferable to rolling on a table for every attack.

There are a lot of people who want to play something unique, detailed and some people who just want the various bits of fluff to help describe their characters. The Complete Series Brown books detailed limited aspects of the 2E game rules, added optional rules, and player kits to play specific versions of a class. Other resource books that used the same format followed, like the Arms and Equipment guide, Of Ships and the Sea, and others. The Historical Reference books (referred to as the green books) allowed players and DMs to approximate historical situations using the AD&D 2E rules.

Well, 1E had box sets as well, but they really became prolific in 2E. The box sets offered new worlds, new developments in some worlds, and fluff the likes of which are hard to match even today. Masque of The Red Death, Planescape, and Dark Sun are notable campaign setting box sets.

Early in the 2E cycle, TSR decided that instead of releasing book after book of monsters, they would sell a huge binder with the basic monsters in it, and sell packs of sheets to fill it with. Each box set would have sheets with monsters specific to the setting in it, and "galleries" of NPCs and special monsters. They called the binder the Monstrous Compendium, and they eventually released a second binder anyway. It was still much cheaper than publishing books. Eventually TSR would listen to demand and release a basic Monstrous Manual with the most common critters in it. After the cessation of the binder production, new printings of box sets would have little paperback supplements to the monster manuals instead of the punched sheets.

After the mess from Patricia Pulling and Jack Chick, Lorraine Williams decided to have Demons and Devils pulled from AD&D 2E. The designers snuck them back in, but changed the names to Tanar'ri and Baatezu. Most players referred to them as Demons and Devils though, until the new names gained more proliferation in TSR branded novels. (Specifically, ones about a Balor and a Gary Stu munchk-assed Drow.)

At least two 2e supplements (Diablo: The Awakening, which is surprisingly a good supplement for non-Diablo campaigns, aside from the item tables, and Van Richten's Guide to Fiends) make reference to demons, however.

Lorraine thought they were ugly. Seriously. Unpleasantness on the part of the player was nixed. It's the same reason the Assassin class went buh-bye.
Half-orcs made a useless, underpowered return in the Complete Book of Humanoids. A powerful and barely changed version of the assassin shows up in The Scarlet Brotherhood.

If 1E lacked fluff, 2E had too much. From specific campaign setting spell books like Pages from the Mages, to the Book of Artifacts, Encyclopedia Magica and the Priest and Mage Spell Compendium series. You also had Dungeon cards, Racial supplementals, etc.
The goal of many of these books was to increase the variety and help DMs create unique and interesting worlds using the examples within as a starting point to make their own. There were no real rules about creating this content due to the designers expecting people to actually think about what they're doing so it was very easy to have DMs make some absolutely broken or truly unique and fun.

The Option series brought in several piecemeal procedures for character and scenario creation. Due to a no-playtesting policy at TSR, many builds under the OPTION books can be horribly broken. Allow these at your own risk, DMs. OPTION Series books are often referred to as 2.5 by newbies looking for some sense of revenge after 2E fans made fun of them when Wizards released 3.5. It's not 2.5; none of the core books are invalidated or changed. The OPTIONs are broken, but they still require the 2E core books and as such are still 2E, much as it pains most fans to admit it.
Although there are broken class combinations possible under the Option series assuming the DM ignores the fact that he is supposed to provide oversight (notably, it's possible to make a priest character who can use Meteor Swarm as an at-will ability), the series also introduces or reintroduces balanced and archetypal classes such as the Monk, Crusader and Shaman and provides critical special abilities for level 10+ characters.
Amongst the latter, the Hardiness ability, usable by fighters, paladins, and rangers, allows those characters to delay more "unfair" attack forms such as instant death, paralysis, energy drain and mind control spells briefly, and then to sleep off the effects. Many aspects of these books, such as Combat & Tactics combat systems, and many of the options from High Level Campaigns, made it into 3e.

The game had amazing product and lots of fluff. However the business plan was pretty shit. The combination of high quality materials, low relative selling cost, the glut of settings and material for them, the broken gameplay issues later on due to the no-playtesting policy, meant that TSR basically wrote its own ticket to failure. Still, the game plodded on for an amazing 11 years until Dungeons & Dragons 3rd Edition was released.